Micromechanical inertial sensors are increasingly being used for detecting rotational motions in aircraft, automobiles, and other applications because of their extreme ruggedness and small size. Micromechanical inertial sensors also offer potentially significant cost advantages over competing technologies, and have the further advantage that a number of the sensors can be fabricated simultaneously.
A micromechanical gyro is known from U.S. Pat. No. 5,349,855 issued to Bernstein et al., the disclosure of which is incorporated herein by reference. The micromechanical gyro of Bernstein is a micromachined structure fabricated using a dissolved silicon wafer process with boron diffusion and dry etch process steps to define the final dimensions of the structure. The structure includes a pair of tuning fork elements which are electrostatically driven with opposite oscillatory phases such that they vibrate in a plane back and forth in a direction orthogonal to a sensing axis of the gyro. Rotation of the micromechanical gyro about its sensing axis causes the vibrating elements to experience Coriolis forces which make the elements vibrate out of the plane of their forced vibratory motion. The deflection of the elements out of this plane is detected and electronically converted into a measure of the rotational rate of the gyro.
The vibrating tuning fork elements, also known as proof masses, are suspended between a pair of structures that are mechanically grounded to a substrate of the gyro. The ends of the proof masses are connected to the mechanically grounded structures by beams which are etched out of the silicon wafer and are integrally formed with the proof masses.
One of the problems associated with micromechanical inertial sensors such as the type described in the Bernstein patent is that the proof masses are driven with relatively large amplitude vibrations relative to the lengths of the beams which attach the proof masses to the fixed structures. For example, the vibratory amplitude may be 20 percent of the beam length. Under these circumstances, the beams are deflected to relatively large angles, such that the stretching of the beams in their length direction is no longer negligible. Because the beams are generally much stiffer in their length direction than they are in bending, the result is that the restoring or spring force of each beam becomes nonlinear with the proof mass deflection in the vibratory direction. Consequently, the apparent natural resonant frequency of the proof mass becomes dependent on the vibration amplitude.